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Appendix //.

and discharged along C D, the pressure again falling to A. The work
done on the air is the area A B C D. Similarly, in the motor, we admit
along D G, expand from G to H, and discharge along H A, the pressure
rising again to D. The work done by the air is D G H A.

work returned       D G H A

work expended      A B C D
and these areas are to be measured.    For any pressure P,    P Vv = C


" *   P Vby     Cb

and a = a constant


which is true anywhere on the adiabatics.    Imagine the areas cut
into horizontal strips, each of a very small width c^ and let a = area of

one strip to Va, while b is that to Vb.    Then a = cVn and I) =
Sum the strips for the whole areas, and let Va == R Vb.

2Vb   ^   i_ = Vb
" sVbR      "R      V"

Area D G H A      V

Area A 3 C D      Va~

and, = V;

Now suppose ratio of compression   ~1 = r

Then by p 607


But, by changing from r2 at c to TJ at G by constant pressure, we
have, by Charles' law:

and ri